This invention relates to a rotating birefringent-plate ellipsometer and its application to photoelasticimetry. In other words, the present invention relates to a process and apparatus for analyzing the polarization components of incident light as well as processes and apparatus for determining the characteristics of birefringent media onto which a light beam of known polarization is directed.
In the following description of the prior art and of the present invention, the following concepts will be employed:
(1) Characteristic parameters of the states of polarization of a light wave:
A polarized light wave is, in general, polarized elliptically and, in the limit, it is linearly or circularly polarized. The polarization parameters are .alpha. and .lambda.. .alpha. defines the orientation of the major axis of the ellipse with respect to a reference direction, and .lambda. defines the flatness of the ellipse. That is, .lambda. is equal in absolute value to the ratio of the minor axis of the ellipse to the major axis of the ellipse.
(2) Characteristic parameters of a birefringent plate:
A birefringent plate is defined by the orientation .theta. of its fast axis and by the phase shift .phi. produced by the plate between the light vectors moving along the fast axis and along the slow axis of the plate respectively.
For example, for circularly polarized light the parameter .lambda. is equal to .pi./4. If a circularly polarized light beam passes through a birefringent plate of parameters .theta. and .phi., one will have at the output of the plate: EQU 2.alpha.=2.theta.-(.pi./2) EQU cos 2.lambda.=sin .phi..
Linear light is characterized by the fact that the parameter .lambda. is equal to zero. For instance, linear light falling on a birefringent plate of parameters .theta. and .phi. along the bisectors of the axes of this birefringent will, after having passed through the birefringent, become a light wave characterized by the following parameters .alpha. and .lambda.: EQU .alpha.=.theta..+-.(.pi./4) EQU 2.lambda.=.phi.
In the prior art, two principal types of ellipsometers are known; on the one hand, ellipsometers of conventional type in which one proceeds by trying to compensate for an elliptical vibration by means of a variable compensator such as the Babinet compensator, which methods are difficult and lengthy. On the other hand there are automatic processes, such as described in particular in French Pat. No. 1,544,836, and its U.S. counterpart U.S. Pat. No. 3,580,681 in which a polarizer turning in front of a light receiver is employed. Such an automatic apparatus makes it possible to measure cos 2 .lambda. and .alpha., these parameters corresponding to the amplitude of the alternating part of the electric signal obtained by a photodetector and to the phase of the alternating part. One drawback of this method resides in the fact that one obtains a measure of the cosine of 2 .lambda., and not .lambda. directly. In order to solve this problem, as has been stated in the aforesaid patent, a retractable quarter-wave plate can be added to the unit. The method of use then consists of retracting the quarter-wave plate and measuring .alpha. as in the previous case, and then inserting the quarter-wave plate with an orientation corresponding to that of the angle .alpha. measured. Thus, the phase of the component having twice the frequency of the frequency of rotation of the rotating analyzer supplies the parameter .alpha.-.lambda.. However, it will be noted that this second method, which permits a measurement of .lambda. without passing through a sinusoidal function of this parameter, is relatively complicated.
It will also be noted that, in general, in most of the known ellipsometric, polarimetric and photo-elasticimetric devices, only polarizers (or analyzers), quarter-wave plates and half-wave plates are used for all practical purposes as optical components in measuring apparatus. This is due to the fact that the calculations of the states of polarization of light are simplified considerably in the event specific birefringents are used, such as quarter-wave and half-wave plates. This has had the effect of retarding progress in the field of polarimetry since the various apparatus comprising the three fundamental elements mentioned above were successfully developed. One basis for the present invention resides in the use of a formalism which had been neglected in the field of polarimetry, namely the Poincare sphere formalism. This formalism has been reanalyzed and expanded to make it particularly simple to handle, as set forth in particular in the doctoral thesis of Mr. Andre Robert on Mar. 23, 1973, at the Paul Sabatier University in Toulouse. Thus, as will be shown, the apparatus in accordance with the present invention use any birefringent plates other than quarter-wave or half-wave plates. This constitutes a step forward in polarmetric techniques, in which the use of such elements is not believed to have been contemplated up to the present time.
An object of the present invention is to provide a new ellipsometer which permits direct measurement of the parameters .alpha. and .lambda. without passing through a trigonometric function of these parameters, this apparatus being particularly simple.
Another object of the present invention is to contemplate applications of such an ellipsometer to photoelastimetric measurements by reflection or transmission.
Still another object is to provide a photoelasticimeter having two wavelengths to permit measurements of the characteristic parameters of a polarized wave or of a birefringent model to be studied while avoiding the indeterminateness within .pi. radians which is present in the case of measurements carried out with a single wavelength.
In order to achieve these objects, as well as still other objects, the present invention provides an ellipsometer for the measurement of the polarization parameters .alpha. and .lambda. of a light wave comprising a birefringent rotating at a constant angular velocity .omega.; an orientable quarter-wave plate; a polarizer; a photoelectric receiver; means for supplying reference signals of the frequencies 2.omega. and 4.omega.; electronic means for synchronous detection of the output signals of the receiver having the frequencies 2.omega. and 4.omega. in relation to the reference signals, the signal of frequency 2.omega. being cancelled by the quarter-wave plate, the orientation of which then provides an indication of the first parameter; and means for measuring the phase of the signal of frequency 4.omega. thereby supplying an indication of the second parameter.
The present invention also provides special arrangements of the components included in the above ellipsometer to permit analysis of the parameters of a model to be studied, the apparatus receiving a light wave of predetermined polarization. It will be noted that one advantage of the present invention is that only phase measurements and no amplitude measurements are effected. One therefore is not hampered by fluctuations in amplitude of the incident light beam and accordingly it is not necessary to provide amplitude control of this beam nor to take precautionary measures with respect to parasitic light.
In the present specification, the letter ".omega." is used to designate both frequencies and angular frequencies (pulsations) and the expression "birefringent" as a noun is used to designate an element which exhibits birefringence; for instance, a "rotating birefringent" may designate a mechanically rotating birefringent plate or a Kerr cell subjected to a rotating field.